Complex Number equation: $z+2barz= |barz+3|$

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Solve $z+2barz= |barz+3|$.




I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.



**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!







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up vote
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down vote

favorite
1













Solve $z+2barz= |barz+3|$.




I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.



**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!







share|cite|improve this question






















  • The question is no longer open.
    – Paul Frost
    Sep 1 at 0:08












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1






Solve $z+2barz= |barz+3|$.




I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.



**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!







share|cite|improve this question















Solve $z+2barz= |barz+3|$.




I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.



**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 25 at 8:26

























asked Aug 25 at 8:12









Nick

11




11











  • The question is no longer open.
    – Paul Frost
    Sep 1 at 0:08
















  • The question is no longer open.
    – Paul Frost
    Sep 1 at 0:08















The question is no longer open.
– Paul Frost
Sep 1 at 0:08




The question is no longer open.
– Paul Frost
Sep 1 at 0:08










3 Answers
3






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up vote
0
down vote













HINT



Since



$$z+2bar z=|bar z+3|$$



and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve



$$3x=|x+3|$$






share|cite|improve this answer



























    up vote
    0
    down vote













    Let $z=x+iy$ then
    $$(x+iy)+(2x-2iy)=|x-iy+3|$$
    $$3x-iy=|(x+3)-iy|$$
    shows
    $$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
    can you proceed?






    share|cite|improve this answer



























      up vote
      0
      down vote













      Note that $z+2overline z$ must be real, which is only possible if $z$ is real !



      Then $$3x=|x+3|$$



      and $x$ must be positive.



      Finally,



      $$3x=x+3.$$






      share|cite|improve this answer




















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        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes








        up vote
        0
        down vote













        HINT



        Since



        $$z+2bar z=|bar z+3|$$



        and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve



        $$3x=|x+3|$$






        share|cite|improve this answer
























          up vote
          0
          down vote













          HINT



          Since



          $$z+2bar z=|bar z+3|$$



          and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve



          $$3x=|x+3|$$






          share|cite|improve this answer






















            up vote
            0
            down vote










            up vote
            0
            down vote









            HINT



            Since



            $$z+2bar z=|bar z+3|$$



            and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve



            $$3x=|x+3|$$






            share|cite|improve this answer












            HINT



            Since



            $$z+2bar z=|bar z+3|$$



            and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve



            $$3x=|x+3|$$







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Aug 25 at 8:17









            gimusi

            70k73786




            70k73786




















                up vote
                0
                down vote













                Let $z=x+iy$ then
                $$(x+iy)+(2x-2iy)=|x-iy+3|$$
                $$3x-iy=|(x+3)-iy|$$
                shows
                $$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
                can you proceed?






                share|cite|improve this answer
























                  up vote
                  0
                  down vote













                  Let $z=x+iy$ then
                  $$(x+iy)+(2x-2iy)=|x-iy+3|$$
                  $$3x-iy=|(x+3)-iy|$$
                  shows
                  $$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
                  can you proceed?






                  share|cite|improve this answer






















                    up vote
                    0
                    down vote










                    up vote
                    0
                    down vote









                    Let $z=x+iy$ then
                    $$(x+iy)+(2x-2iy)=|x-iy+3|$$
                    $$3x-iy=|(x+3)-iy|$$
                    shows
                    $$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
                    can you proceed?






                    share|cite|improve this answer












                    Let $z=x+iy$ then
                    $$(x+iy)+(2x-2iy)=|x-iy+3|$$
                    $$3x-iy=|(x+3)-iy|$$
                    shows
                    $$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
                    can you proceed?







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Aug 25 at 8:17









                    Nosrati

                    21.4k41746




                    21.4k41746




















                        up vote
                        0
                        down vote













                        Note that $z+2overline z$ must be real, which is only possible if $z$ is real !



                        Then $$3x=|x+3|$$



                        and $x$ must be positive.



                        Finally,



                        $$3x=x+3.$$






                        share|cite|improve this answer
























                          up vote
                          0
                          down vote













                          Note that $z+2overline z$ must be real, which is only possible if $z$ is real !



                          Then $$3x=|x+3|$$



                          and $x$ must be positive.



                          Finally,



                          $$3x=x+3.$$






                          share|cite|improve this answer






















                            up vote
                            0
                            down vote










                            up vote
                            0
                            down vote









                            Note that $z+2overline z$ must be real, which is only possible if $z$ is real !



                            Then $$3x=|x+3|$$



                            and $x$ must be positive.



                            Finally,



                            $$3x=x+3.$$






                            share|cite|improve this answer












                            Note that $z+2overline z$ must be real, which is only possible if $z$ is real !



                            Then $$3x=|x+3|$$



                            and $x$ must be positive.



                            Finally,



                            $$3x=x+3.$$







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered Aug 25 at 8:22









                            Yves Daoust

                            113k665207




                            113k665207



























                                 

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